Reduce to lowest terms: $ \dfrac{7}{4} \div - \dfrac{5}{2} = {?}$
Answer: Dividing by a fraction is the same as multiplying by the reciprocal of the fraction. The reciprocal of $- \dfrac{5}{2}$ is $- \dfrac{2}{5}$ Therefore: $ \dfrac{7}{4} \div - \dfrac{5}{2} = \dfrac{7}{4} \times - \dfrac{2}{5} $ $ \phantom{ \dfrac{7}{4} \times - \dfrac{2}{5}} = \dfrac{7 \times -2}{4 \times 5} $ $ \phantom{ \dfrac{7}{4} \times - \dfrac{2}{5}} = \dfrac{-14}{20} $ The numerator and denominator have a common divisor of $2$, so we can simplify: $ \dfrac{-14}{20} = \dfrac{-14 \div 2}{20 \div 2} = -\dfrac{7}{10} $